We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolu tion equation. We take the (3+ 1)-dimensional potential-YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional potential-YTSF equa tion into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.